Detailed measurements within the separated shear layer behind a flat plate normal to an airflow are reported. A long, central splitter plate in the wake prevented vortex shedding and led to an extensive region of separated flow with mean reattachment some ten plate heights downstream. The Reynolds number based on plate height was in excess of 2 × 1044.

Extensive use of pulsed-wire anemometry allowed measurements of all the Reynolds stresses throughout the flow, along with some velocity autocorrelations and integral timescale data. The latter help to substantiate the results of other workers obtained in separated flows of related geometry, particularly in the identification of a very low-frequency motion with a timescale much longer than that associated with the large eddies in the shear layer. Wall-skin-friction measurements are consistent with the few similar data previously published and indicate that the thin boundary layer developing beneath the separated region has some ‘laminar-like’ features.

The Reynolds-stress measurements demonstrate that the turbulence structure of the separated shear layer differs from that of a plane mixing layer between two streams in a number of ways. In particular, the normal stresses all rise monotonically as reattachment is approached, are always considerably higher than the plane layer values and develop in quite different ways. Flow similarity is not a useful concept. A major conclusion is that any effects of stabilizing streamline curvature are weak compared with the effects of the re-entrainment at the low-velocity edge of the shear layer of turbulent fluid returned around reattachment. It is argued that the general features of the flow are likely to be similar to those that occur in a wide range of complex turbulent flows dominated by a shear layer bounding a large-scale recirculating region.

Using the method of matched asymptotic expansions, the interaction between axisymmetric laminar boundary layers and supersonic external flows is investigated in the limit of large Reynolds numbers. Numerical solutions to the interaction equations are presented for flare angles α that are moderately large. If α > 0 the boundary layer separates upstream of the corner and the formation of a plateau structure similar to the two-dimensional case is observed. In contrast to the case of planar flow, however, separation can occur also if α < 0, owing to the axisymmetric effect of overexpansion and recompression. The separation point then is located downstream of the corner and, most remarkable, a hysteresis phenomenon is observed.

A theoretical investigation into the next stage of dynamic stall, concerning the beginnings of eddy shedding from the boundary layer near an aerofoil's leading edge, is described by means of the unsteady viscous-inviscid interacting marginal separation of the boundary layer. The fully nonlinear stage studied in the present paper is shown to match with a previous ‘weakly nonlinear’ regime occurring in the earlier development of the typical eddy from its initially slender thin state. Numerical solutions followed by linear and nonlinear analysis suggest that with confined initial conditions the strong instabilities in the present unsteady flow tend to force a breakdown within a finite time. This leads on subsequently to an unsteady predominantly inviscid stage where the eddy becomes non-slender, spans the entire boundary layer and its evolution then is governed by the Euler equations. This is likely to be followed by the shedding of the eddy from the boundary layer.

It is known that the classical boundary-layer solution breaks down through the appearance of the Goldstein singularity in a steady solution or Van Dommelen's singularity in an unsteady solution. Interaction between the inviscid flow and the boundary layer removes the Goldstein singularity, until a new critical parameter is reached, corresponding to a marginal separation in the asymptotic triple-deck description. In earlier studies instabilities were encountered in interacting boundary-layer calculations of steady flow along an indented plate, which might be related to the breakdown of the marginal separation. The present study identifies them as numerical. Further, until now it was unknown whether the unsteady interacting boundary-layer approach would remove Van Dommelen's singularity in the classical boundary layer around an impulsively started cylinder. It is shown here that its appearance is at least delayed. The calculations show the experimentally known individualization of a vortex, after which the solution grows without reaching a steady limit; a process that is likely to be related to dynamic stall.

An analytical investigation of the stability of a viscous, annular liquid jet moving in an inviscid medium is presented. This problem is a generalization of the well-known cases of a round cylindrical jet (obtained here when the ratio of internal to external radii tends to zero) and the flat thin liquid sheet (when the ratio above tends to unity). A critical ‘penetration’ thickness T is defined. When the annulus thickness is greater than T, the annular jet behaves like a full liquid jet; the only unstable perturbations are axisymmetric, and their growth rate is independent of thickness. When the annulus thickness is less than T, the jet behaves like a two-dimensional liquid sheet; the most unstable perturbations are antisymmetric and their growth rate increases as the jet thickness decreases. Therefore, an annular liquid jet with a sufficiently small ring thickness will disintegrate into spherical shells much faster than a full liquid jet disintegrates into drops, in accordance with existing experimental data. Non-dimensional expressions for the penetration thickness are given for both viscous and inviscid jets.

The orbital motions in surface gravity waves are of interest for analysing wave records made by accelerometer buoys. In this paper we derive some exact expressions for the first, second and third cumulants of the vertical orbital displacements in a regular Stokes wave of finite amplitude in terms of previously known integral quantities of the wave: the kinetic and potential energies, the phase speed c and the mass-transport velocity U at the free surface. These results generalize a remarkably simple relation found previously between the Lagrangian-mean surface level and the product Uc.

Expansions are given in powers of the wave steepness parameter ak which show that the third Lagrangian cumulant is very small – of order (ak)6, indicating a high degree of vertical symmetry in the orbit. This contrasts with the situation in random waves, where the third cumulant is of order (ak)4 only. It is shown that the increased skewness in random waves is due mainly to an O(ak)2 shift in the Lagrangian mean level of individual waves. Such shifts in mean level may be too gradual to be fully detected by some accelerometer buoys. In that case the apparent skewness will be reduced.

The first 27 terms in a series expansion for the profile of a solitary wave are computed. From this, series expansions for the wave amplitude, mass and potential energy are obtained. A previous study indicated that the partial sums of these series converged for small- to medium-amplitude waves and that the diagonal Padé approximants converged for waves of all amplitudes. The data derived here show that this is not the case and that apparent convergence of Padé approximants can be misleading.